• Bulletin of the Korean Mathematical Society
• /
• v.34 no.1
• /
• pp.51-61
• /
• 1997

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.4
• /
• pp.787-792
• /
• 2010

Let A and B be some standard operator algebras on complex Banach spaces X and Y, respectively. We give the concrete forms of linear idempotence preserving maps $\Phi\;:\;A\;{\rightarrow}\;B$ on finite-rank operators.

• Journal of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.353-365
• /
• 1994

During the past century, one of the most active and continuing subjects in matrix theory has been the study of those linear operators on matrices that leave certain properties or subsets invariant. Such questions ar usually called "Linear Preserver Problems".

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.3
• /
• pp.501-507
• /
• 2005

A Boolean matrix with rank 1 is factored as a left factor and a right factor. The perimeter of a rank-1 Boolean matrix is defined as the number of nonzero entries in the left factor and the right factor of the given matrix. We obtain new characterizations of rank preservers, in terms of perimeter, of Boolean matrices.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.2
• /
• pp.283-287
• /
• 2002

In this paper, we will investigate the set of linear operators on real square matrices that strongly preserve multivariate majorisation without any additional conditions on the operator. This answers earlier conjecture on nonnegative matrices in [3] .

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.335-342
• /
• 1996

Suppose $k$ is a field and $M$ is the set of all $m \times n$ matrices over $k$. If T is a linear operator on $M$ and f is a function defined on $M$, then T preserves f if f(T(A)) = f(A) for all $A \in M$.

• Journal of the Korean Mathematical Society
• /
• v.47 no.4
• /
• pp.805-818
• /
• 2010

We classify linear maps which preserve idempotents on $n{\times}n$ matrices over some classes of semirings. Our results include many known semirings like the semiring of all nonnegative integers, the semiring of all nonnegative reals, any unital commutative ring, which is zero divisor free and of characteristic not two (not necessarily a principal ideal domain), and the ring of integers modulo m, where m is a product of distinct odd primes.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.311-318
• /
• 1996

For positive integral vectors $R = (r_1, \cdots, r_m)$ and $S = (s_1, \cdots, s_n)$, we consider the class $U(R,S)$ of all $m \times n$ matrices of 0's and 1's with the row sum vector R and the column sum vector S.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.277-287
• /
• 2017

We consider ${\tau}_{\infty}(F)$ - the space of upper triangular infinite matrices over a field F. We investigate injective linear maps on this space which preserve the additivity of rank, i.e., the maps ${\phi}$ such that rank(x + y) = rank(x) + rank(y) implies rank(${\phi}(x+y)$) = rank(${\phi}(x)$) + rank(${\phi}(y)$) for all $x,\;y{\in}{\tau}_{\infty}(F)$.

• Kyungpook Mathematical Journal
• /
• v.46 no.1
• /
• pp.89-96
• /
• 2006

For a rank-1 matrix A, there is a factorization as $A=ab^t$, the product of two vectors a and b. We characterize the linear operators that preserve rank and some equivalent condition of rank-1 matrices over a chain semiring. We also obtain a linear operator T preserves the rank of rank-1 matrices if and only if it is a form (P, Q, B)-operator with appropriate permutation matrices P and Q, and a matrix B with all nonzero entries.